Cruxes I Have With Many LW Readers

There's a crux I seem to have with a lot of LWers that I've struggled to put my finger on for a long time but I think reduces to some combination of:

• faith in elegance vs. expectation of messiness;
• preference for axioms vs. examples;
• identification as primarily a scientist/truth-seeker vs. as an engineer/builder.

I tend to be more inclined towards the latter in each case, whereas I think a lot of LWers are inclined towards the former, with the potential exception of the author of realism about rationality [LW · GW], who seems to have opinions that overlap with many of my own. While I still feel uncomfortable with the above binaries, I've now gathered enough examples to at least list them as evidence for what I'm talking about.

Example 1: Linear Algebra Textbooks

A few [LW · GW] LWers [LW · GW] have positively reviewed Linear Algebra Done Right (LADR), in particular complimenting it for revealing the inner workings of Linear Algebra. I too recently read most of this book and did a lot of the exercises. And... I liked it but seemingly less than the other reviewers. In particular, I enjoyed getting a lot of practice reading definition-theorem-proof style math and doing lots of proofs myself, but found myself wishing for more examples and discussion of how to compute things like eigenvalues in practice. While I know that's not what the book's about, the difference I'm pointing to is more that I found the omission of these things bothersome, whereas I suspect the other reviewers were happy with the focus on constructing the different objects mathematically (I'm also obviously making some assumptions here).

On the other hand, I've recently been reading sections of Shilov's Linear Algebra, which is more concrete but does more ugly stuff like present the determinant very early on, and I feel like I'm learning better from it.

I think one contributing factor towards this preference difference is that I tend to be more OK with unmotivated messiness if the messy thing is clearly useful for something but less OK slogging through a bunch of elegant but not-clear-what-it's-used-for build up. Another way to put this would be that I tend to like to get top-down view of a subject and then go depth-first afterwards, whereas others seem happy to learn bottom-up. I used to think this was because of my experience with programming where algorithms are pretty much always presented in
terms of their purpose and tend to be become messier as they get optimized for performance. I still like knowing the motivation for things, but I also accept that stuff that works for real applications often has a bunch of messiness. On the other hand, a lot of LWers are also programmers who are only now going deep on math and they seem to still be happy with the axiomatic math way of doing things. So having a programming background doesn't seem to correlate with my preferences that strongly...

What would be great would be if someone would chime in providing better hypotheses/explanations than the one I've given.

Example 2: Scientists vs. Engineers as Role Models

Much of early LW content, the Sequences in particular, used scientists like Einstein and Feynman as role models in discussions (and also targets of criticism in fairness). While I love Feynman and Einstein too, I tend to also revere builders/engineers, such as John Carmack, Jeff Dean, and Konrad Zuse, but these types of people don't seem to get nearly as much praise on LW.

One explanation for this is that great but not necessarily thoughtful engineers can drive X-risk through their work. For example, here's [LW(p) · GW(p)] a discussion where a few folks argue that AGI requires insight more than programming ability and explicitly mention needing Judea Pearl more than John Carmack. While this is a fair argument, I'm skeptical that it's the true rejection. Security mindset seems to be as common among engineers as it is among scientists given that most of the folks who participate in things like DefCon and work in computer security tend to be hardcore engineer types like Trammell Hudson. (In his original essay, Eliezer cites Bruce Schneier, definitely an engineer, as someone he trusts to have security mindset.)

Another potential explanation for this is that LW readers tend to like doing and learning about science (pure math included) more than doing engineering. It's plausible that people who were attracted to early LW/OB content and were compelled by arguments for X-risk tend to also prefer science to engineering.

Conclusion

Unfortunately, I don't have some sort of nice insight to conclude this with. I don't think the differences between my and other LWers preferences are bad so much as an implicit thing that doesn't get discussed.

I am curious whether my dichotomies seem reasonably accurate to anyone reading this? And if so, do my hypotheses for them seem reasonable?

Anki's Not About Looking Stuff Up

Attention conservation notice: if you've read Michael Nielsen's stuff about Anki, this probably won't be new for you. Also, this is all very personal and YMMV.

In a number of discussions of Anki here and elsewhere, I've seen Anki's value measured in terms of time saved by not having to look stuff up. For example, Gwern's spaced repetition post includes a calculation of when it's worth it to Anki-ize threshold, although I would be surprised if Gwern hasn't already thought about the claim going to make.

While I occasionally use Anki to remember things that I would otherwise have to Google, e.g. statistics, I almost never Anki-ize things so that I can avoid Googling them in the future. And I don't think in terms of time saved when deciding what to Anki-ize.

Instead, (as Michael Nielsen discusses in his posts) I almost always Anki-ize with the goal of building a connected graph of knowledge atoms about an area in which I'm interested. As a result, I tend to evaluate what to Anki-ize based on two criteria:

1. Will this help me think about this domain without paper or a computer better?
2. In the Platonic graph of this domain's knowledge ontology, how central is this node? (Pedantic note: it's easier to visualize distance to the root of the tree, but this requires removing cycles from the graph.)

To make this more concrete, let's look at an example of a topic I've been Anki-izing recently, causal inference. I just started Anki-izing this topic a week ago, so it'll be easier for me to avoid idealizing the process. Looking at my cards so far, I have questions about and definitions of things like "d-separation", "sufficient/admissible sets", and "backdoor paths". Notably, for each of these, I don't just have a cloze card to recall the definition, I also have image cards that quiz me on examples and conceptual questions that clarify things I found confusing upon first encountering these concepts. I've found that making these cards has the effect of both forcing me to ensure I understand concepts (because writing cards requires breaking them down) and makes it easier to bootstrap my understanding over the course of multiple days. Furthermore, knowing that I'll remember at least the stuff I've Anki-ized has a surprisingly strong motivational impact on me on a gut level.

All that said, I suspect there are some people for whom Anki-izing wouldn't be helpful.

The first is people who have the time and a career in which they focus on a narrow enough set of topics such that they repeatedly see the same concepts and rarely go for long periods without revisiting them. I've experienced this myself for Python - I learned it well before starting to use Anki and used it every day for many years. So even if I forget some stuff, it's very easy for me to use the language fluently after time away from it.

The second is, for lack of a better term, actual geniuses. Like, if you're John Von Neumann and you legitimately have an approximation of a photographic memory (I'm really skeptical that he actually had an eidetic memory but regardless...) and can understand any concept incredibly quickly, you probably don't need Anki. Also, if you're the second coming if John Von Neumann and you're reading this, cool!

To give another example, Terry Tao is a genius who also has spent his entire life doing math. Probably doesn't need Anki (or advice from me in general in case it wasn't obvious).

Finally, I do think how to use Anki well is an under-explored topic given that there's on the order of 10 actual blog posts about it. Given this, I'm still figuring things out myself, in particular around how to Anki-ize stuff that's more procedural, e.g. "when you see a problem like this, consider these three strategies" or something. If you're also experimenting with Anki, I'd love to hear from you!

Weird thing I wish existed: I wish there were more videos of what I think of as 'math/programming speedruns'. For those familiar with speedrunning video games, this would be similar except the idea would be to do the same thing for a math proof or programming problem. While it might seem like this would be quite boring since the solution to the problem/proof is known, I still think there's an element of skill to and would enjoy watching someone do everything they can to get to a solution, proof, etc. as quickly as possible (in an editor, on paper, LaTex, etc.).

This is kind of similar to streaming ACM/math olympiad competition solving except I'm equally more in people doing this for known problems/proofs than I am for tricky but obscure problems. E.g., speed-running the SVD derivation.

While I'm posting this in the hope that others are also really interested, my sense is that this would be incredibly niche even amongst people who like math so I'm not surprised it doesn't exist...

Watching my kitten learn/play has been interesting from a "how do animals compare to current AIs perspective?" At a high level, I think I've updated slightly towards RL agents being further along the evolutionary progress ladder than I'd previously thought.

I've seen critiques of RL agents not being able to do long-term planning as evidence for them not being as smart as animals, and while I think that's probably accurate, I have noticed that my kitten takes a surprisingly long time to learn even 2-step plans. For example, when it plays with a toy on a string, I'll often try putting the toy on a chair that it only knows how to reach by jumping onto another chair first. It took many attempts before it learned to jump onto the other chair and then climb to where I'd put the toy, even though it had previously done that while exploring many times. And even then, it seems to be at risk of "catastrophic forgetting" where we'll be playing in the same way later and it won't remember to do the 2-step move. Related to this, its learning is fairly narrow even for basic skills, e.g. I have 4 identical chairs around a table but it will be afraid of jumping onto one even though it's very comfortable jumping onto another.

Now part of this may be that cats are known for being biased towards trial-and-error compared to other similarly-sized mammals like dogs (see Gwern's write-up for more on this) and that adult cats may be better than kittens at "long-term" planning. However, a lot of critiques of RL, such as Josh Tenenbaum's, argue that our AIs don't even compare to young children in terms of their abilities. This is undoubtedly true with respect to ability to actually move around in the world, grasp objects, etc. but seems less true than I'd previously thought with respect to "higher level" cognitive abilities such as planning. To make this more concrete, I'm skeptical that my kitten could currently succeed at a real life analogue to Montezuma's Revenge.

Another thing I've observed relates to some recent work by Konrad Kording, Adam Marblestone, and Greg Wayne on integrating deep learning and neuroscience. They postulate that due to the genomic bottleneck, it's plausible that brains leverage heterogeneous, evolving cost functions to do semi-supervised learning throughout development. While much more work needs to be done investigating this hypothesis (as acknowledged by the authors), it does ring true with some of my observations of my kitten. In particular, I've noticed that it recently became much more interested in climbing things and jumping on objects on its own, whereas previously I couldn't even get it to using treats. This seems like a plausible example of a "switch" being flipped that increased reward for being high up (or something, obviously this is quite hand-wavy).

I'm trying to come up with predictions that I can make regarding the next few months based on these two initial observations but don't have any great ideas yet.

I keep seeing rationalist-adjacent discussions on Twitter that seem to bottom out with the arguments of the general (very caricatured, sorry) form: "stop forcing yourself and get unblocked and then X effortlessly" where X equals learn, socialize, etc. In particular, a lot of focus seems to be on how children and adults can just pursue what's fun or enjoyable if they get rid of their underlying trauma and they'll naturally learn fast and gravitate towards interesting (but also useful in the long term) topics, with some inspiration from David Deutsch.

On one hand, this sounds great, but it's so foreign to my experience of learning things and seems to lack the kind of evidence I'd expect before changing my cognitive strategies so dramatically. In fairness, I probably am too far in the direction of doing things because I "should", but I still don't think going to the other extreme is the right correction.

In particular, having read Mason Currey's Daily Rituals, I have a strong prior that even the most successful artists and scientists are at risk of developing akrasia and need to systematize their schedules heavily to ensure that they get their butts in the chair and work. Given this, what might convince me would be if someone catalogue of thinkers who did interesting work, quotes or stories that provide evidence that they did what was fun, and counter-examples to show that it's not cherry-picking.

The above is also is related to the somewhat challenged but still I think somewhat valid idea that getting better at things requires deliberate practice, which is not "fun". This also leads me to a subtle point which is that I think "fun" may be being used in a non-standard way by people who claim that learning can always be "fun". I.e. I can see how even not necessarily enjoyable in the moment practice can be something one values on reflection, but this seems like a misuse of the term "fun" to me.

Interesting Bill Thurston quote, sadly from his obituary:

I’ve always taken a “lazy” attitude toward calculations. I’ve often ended up spending an inordinate amount of time trying to figure out an easy way to see something, preferably to see it in my head without having to write down a long chain of reasoning. I became convinced early on that it can make a huge difference to find ways to take a step-by-step proof or description and find a way to parallelize it, to see it all together all at once—but it often takes a lot of struggle to be able to do that. I think it’s much more common for people to approach long case-by-case and step-by-step proofs and computations as tedious but necessary work, rather than something to figure out a way to avoid. By now, I’ve found lots of “big picture” ways to look at the things I understand, so it’s not as hard.

To prevent mis-interpretation, I think people often look at quotes like this (I've seen similar ones about Feynman) and think "ah yes, see anyone can do it". But IME the thing he's describing is much harder to achieve than the "case-by-case"/"step-by-step" stuff.

Blockchain idea inspired by 80,000 Hours's interview of Vitalik Buterin: a lot of podcasts either have terrible transcriptions or presumably pay a service to transcribe their sessions. However, even these services make minor typos such as "ASX" instead of "ASICs" in the linked interview.

Now, most people who read these transcripts presumably notice at least a subset of these typos but don't want to go through the effort of emailing podcasters to tell them about it. On the flip side, there's no good way for hosts to scalably audit flagged typos to see if they're actually typos. What we really want is a mostly automated mechanism to aggregate flagged typos and accept fixes which multiple people agree upon that only pays people (micro amounts) for correctly identifying typos.

This mechanism seems like something that could live on a blockchain in some sort of smart contract. Obviously, like almost every blockchain application, you *could* do it without a blockchain, but using blockchain makes it easy to audit and distribute the micro-payments rather than having to program the voting scheme from scratch on top of a centralized database.

I've recently been obsessing over the idea of trying to "make math more like programming". I'm not sure if it's just because I feel fluent at programming and still not very fluent at abstract math or also because programming really does have a feedback loop that you don't get in math.

Regardless, based on my reading it seems like there's a general consensus in math that even the most modern theorem provers, like Lean and Coq, are much less efficient than typical "informal" math reasoning. That said, I wonder if this ignores some of the benefits that programmers get from writing in a formal language, i.e. automatic refactoring tools, fast feedback loops, and code analysis/search tools. Also, it seems like a sufficiently user-friendly math theorem proving tool could be useful for education. If kids can learn how to program in Javascript, I have to believe they can learn to prove theorems, even if the learning curve's relatively steep.

Maybe once I play around with Lean more, I'll change my mind, but for now, I'm sticking to my contrarian viewpoint.

I've been reading a bit about John Conway since his (unfortunate) death. One thing I keep noticing is that everyone seems to emphasize how core having fun was to John Conway's way of doing math. One question I'm interested in in general is how important fun and curiosity [LW · GW] are for doing good research.

I've considered posting a question about this that uses John Conway as an example of someone who 1) was genuinely curious and fun-loving but 2) also had other gifts that played a large role in his ability to do great math. But, I don't want to be insensitive given that he only recently died.

I am considering using Feynman as an example instead as someone who cultivated a reputation for just having fun but had other gifts which played a large role in his success, but I feel a little weird that Conway was the person who originally triggered the thought.

Anyone who reads my shortform have an idea for how I can ask this in a tasteful way?

It seems like (unless I just haven't discovered it yet) there's a sore need for a framework for causal model comparison, analogous to Bayesian model comparison. If you read Pearl (and his students), they rightfully point out that you can't get causal claims without causal assumptions but don't talk much about how you actually formulate the causal model in the first place ("domain knowledge"). As a result, if you look at the literature, researchers mostly seem to use a small set of causal models that may or may not describe phenomena, e.g. the classic "instrumental variable" graph, for inference.

I view this as analogous to selecting a prior in applied Bayesian modeling. However, there there's a nice set of tools [LW · GW] for comparing how likely different models are, whereas I'm not aware of any such thing in the causal inference world. There's something called "sensitivity analysis" but that's about how much deviation from your assumptions affects your conclusions.

Epistemic status: Thinking out loud.

Introducing the Question

Scientific puzzle I notice I'm quite confused about: what's going on with the relationship between thinking and the brain's energy consumption?

On one hand, I'd always been told that thinking harder sadly doesn't burn more energy than normal activity. I believed that and had even come up with a plausible story about how evolution optimizes for genetic fitness not intelligence, and introspective access is pretty bad as it is, so it's not that surprising that we can't crank up our brains energy consumption to think harder. This seemed to jive with the notion that our brain's putting way more computational resources towards perceiving and responding to perception than abstract thinking. It also fit well with recent results calling ego depletion into question and into the framework in which mental energy depletion is the result of a neural opportunity cost calculation [LW · GW].

Going even further, studies like this one left me with the impression that experts tended to require less energy to accomplish the same mental tasks as novices. Again, this seemed plausible under the assumption that experts brains developed some sort of specialized modules over the thousands of hours of practice they'd put in.

I still believe that thinking harder doesn't use more energy, but I'm now much less certain about the reasons I'd previously given for this.

Chess Players' Energy Consumption

This recent ESPN (of all places) article about chess players' energy consumption during tournaments has me questioning this story. The two main points of the article are:

1. Chess players burn a lot of energy during tournaments, potentially on the order of 6000 calories a day (that's about what marathon runners burn in a day). This results from intense mental stress leading to an elevated heart rate and, as a result, increased oxygen consumption. Chess players also tend to eat less during competitions, which also contributes to weight loss during tournaments (apparently Karpov once lost 20 pounds during an extended chess championship).
2. Chess players and their coaches now understand that humans aren't Cartesian, i.e. our physical health impacts our cognitive performance, and have responded accordingly with intense physical training regimens. On the surface, none of this contradicts the claims I cited above. The article's claiming that chess players burn more energy purely from the side effects of stress, not because their brains are doing more work. So why am I revisiting this question?

Gaps in the Evolutionary Justification

First, reading the chess article led me to notice a big gap in the explanation I gave above for why we shouldn't expect a connection between thinking hard and energy consumption. In my explanation, I mentioned that we should expect our brains to spend much more energy on perceptive and reactive processing than on abstract thinking. This still makes sense to me as a general claim about the median mammal, but now seems less plausible to me as it relates to humans specifically. This recent study, for example, provides evidence that our (humans) big brains are one of two primary causes for our increased energy consumption compared to other primates. As far as I can tell, humans don't seem to have meaningfully better coordination or perceptive abilities than chimps. Chimps have opposable thumbs and big toes, spend their days picking bugs off of each other, and climbing trees. Given this, while I admittedly haven't looked into studies on this but I find it hard to imagine that human brains spend much more energy than chimps on perception.

Let's say that we put aside the question of what exactly human brains use their extra energy for and bucket it into the loose category of "higher mental functions". This still leaves me with a relevant question, why didn't brains evolve to use varying amounts of energy depending on what they were doing? In particular, if we assume that humans are the first and only mammals that spend large fractions of their calories on "extra" brain functions, then why wasn't there selection pressure to have those functions only use energy when they were needed instead of all the time?

Bringing things back to my original point, in my initial story, thinking didn't impact energy consumption because our brains spend most of their energy on other stuff anyway, so there wasn't strong selective pressure to connect thinking intensity to energy consumption. However, I've just given some evidence that "higher brain functions" actually did come with a significant energy cost, so we might expect that those functions' energy consumption would in fact be context-dependent.

Second, it's weird that what we're doing (mentally) can so dramatically impact our energy consumption due to elevated heart rate and other stress-triggered adaptations but has no impact on the energy our brain consumes. To be clear, it makes sense that physical activity and stress would be intimately connected as this connection is presumably very important for balancing the need to eat/escape predators with the need to not use too much energy when sitting around. One doesn't yet make sense to me is that, even though neurons evolved from the same cells as all the rest of our biology, they proved so resistant to optimization for variable energy consumption.

Rescuing the Original Hypothesis

The best explanation I can come up with for the two puzzles I just discussed is that, for whatever reason, evolution didn't select for a neural architecture that could selectively up- and down-regulate its energy consumption depending on the circumstances. For example, maybe the fact that neurons die when they don't have energy is somehow intimately coupled with their architecture such that there's no way to fix it short of something only a goal-directed consequentialist (and therefore not a hill-climbing process) could accomplish. If this is true, even though humans plausibly would've benefited at some point during our evolutionary history from being able to spend more or less energy on thinking, we shouldn't be surprised never happened.

Another weaker (IMO) explanation is that human brains do use more energy in certain situations for some "higher mental functions" but it's not the situations you'd expect. For example, maybe humans use a ton of energy for social cognition and if we could measure the neocortex's energy consumption during parties, we'd find it uses a lot more energy than usual.

ML-related math trick: I find it easier to imagine a 4D tensor, say of dimensions $B\times F\times M\times N$, as a big matrix with dimensions $B\times F$ within which are nested matrices of dimensions $M\times N$. The nice thing about this is, at least for me, it makes it easier to imagine applying operations over the $B\times F$ matrices in parallel, which is something I've had to thing about a number of times doing ML-related programming, e.g. trying to figure out how write the code to apply a 1D convolution-like operation to an entire batch in parallel.

How to remember everything (not about Anki)

In this fascinating article, Gary Marcus (now better known as a Deep Learning critic, for better or worse) profiles Jill Price, a woman who has an exceptional autobiographical memory. However, unlike others that studied Price, Marcus plays the role of the skeptic and comes to the conclusion that Price's memory is not exceptional in general, but instead only for the facts about her life, which she obsesses over constantly.

Now obsessing over autobiographical memories is not something I'd recommend to people, but reading this did make me realize that to the degree it's cultivate-able, continuously mulling over stuff you've learned is a viable strategy for remembering it much better.

Sometimes there are articles I want to share, like this one, where I don't generally trust the author and they may have quite (what I consider) wrong views overall but I really like some of their writing. On one hand, sharing the parts I like without crediting the author seems 1) intellectually / epistemically dishonest and 2) unfair to the author. On the other hand, providing a lot of disclaimers about not generally trusting the author feels weird because I feel uncomfortable publicly describing why I find them untrustworthy.

Not really sure what to do here but flagging it to myself as an issue explicitly seems like it might be useful.

Taking Self-Supervised Learning Seriously as a Model for Learning

It seems like if we take self-supervised learning (plus a sprinkling of causality) seriously as key human functions, we can more directly enhance our learning by doing much more prediction / checking of predictions while we learn. (I think this is also what predictive processing implies but don't understand that framework as well.)

Weird thought I had based on a tweet about gradient descent in the brain: it seems like one under-explored perspective on computational graphs is the causal one. That is, we can view propagating gradients through the computational graph as assessing the effect of an intervention on some variable on all of a nodes' children.

Reason to think this might be useful:

• *Maybe* this can act as a different lens for examining NN training?

Reasons why this might not be useful:

• It's not obvious that it makes sense to think of nodes in an NN (or any differential computational graph) as causally related in the sense we usually talk about in causal inference.
• A causal interpretation of gradients isn't obvious because they're so local, whereas most causal inference focuses on the impact of more non-trivial interventions. OTOH, there are some NN interpretability techniques that try to solve this, so maybe these have better causal interpretations?

If algebra's a deal with the devil where you get the right answer but don't know why, then geometric intuition's a deal with the devil where you always get an answer but don't know whether it's right.

Someone should write the equivalent of TAOCP for machine learning.

(Ok, maybe not literally the equivalent. I mean Knuth is... Knuth. So it doesn't seem realistic to expect someone to do something as impressive as TAOCP. And yes, this is authority worship and I don't care. He's Knuth goddamn it.)

Specifically, a book where the theory/math's rigorous but the algorithms are described in their efficient forms. I haven't found this in the few ML books I've read parts of (Bishop's Pattern Recognition and Machine Learning, MacKay's Information Theory, and Tibrishani et Al's Elements of Statistical Learning), so if it's already out there, let me know.

Note that I don't mean that whoever does this should do the whole MMIX thing and write their own language and VM.

(Removed.)

Link post for a short post I just published describing my way of understanding Simpson's Paradox.

Thing I desperately want: tablet native spaced repetition software that lets me draw flashcards. Cloze deletions are just boxes or hand-drawn occlusions.

Today I attended the first of two talks in a two-part mini-workshop on Variational Inference. It's interesting to think of from the perspective of my recent musings about more science-y vs. engineering mindsets because it highlighted the importance of engineering/algorithmic progress in widening Bayesian methods' applicability

The presenter, who's a fairly well known figure in probabilistic ML and has developed some well known statistical inference algorithms, talked about how part of the reason so much time was spent debating philosophical issues in the past was because Bayesian inference wasn't computationally tractable until the development of Gibbs Sampling in the '90s by Gelfand & Smith.

To be clear, the type of progress I'm talking about is still "scientific" in the sense of it mostly involves applied math and finding good ways to approximate posterior distributions. But, it's "engineering" in the sense that it's the messy sort of work I talked about in my other post, where messy means a lot of the methods don't have a good theoretical backing and involve making questionable (at least ex ante) statistical assumptions. Now, the counter is of course that we don't have a theoretical backing yet, but there still may be one in the future.

I'll probably have more to say about this when the workshop's over but I partly just wanted to record my thoughts while they were fresh.

I'm interested in reading more about what might've been going on in Ramanujan's head when he did math. So far, the best thing I've found is this.